In this work we calculate the different ingredients needed to obtain the matter density profile of the large‐scale structure we observe now a days in a qualitative way. The key difference of the work lays on the fact that we study the formation of structure in the Universe assuming that dark matter can be described by a scalar field (SF) Φ with a quadratic potential V(Φ) = m2Φ2/2. We derive the evolution equations in the linear regime of perturbations, here the scalar perturbations have an oscillating growing mode that could lead to the formation of gravitational structures. We then solve the obtained set of equations like a dynamical system in which we introduce new dimensionless parameters that describe the cosmology of the different studied quantities.